8 found
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  1.  21
    Algebraic Geometry for Mv-Algebras.Lawrence P. Belluce, Antonio di Nola & Giacomo Lenzi - 2014 - Journal of Symbolic Logic 79 (4):1061-1091.
  2.  32
    Algebraically Closed MV-Algebras and Their Sheaf Representation.Antonio Di Nola, Anna R. Ferraioli & Giacomo Lenzi - 2013 - Annals of Pure and Applied Logic 164 (3):349-355.
    In this paper we first provide a new axiomatization of algebraically closed MV-algebras based on McNaughtonʼs Theorem. Then we turn to sheaves, and we represent algebraically closed MV-algebras as algebras of global sections of sheaves, where the stalks are divisible MV-chains and the base space is Stonean.
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  3.  28
    Representation of MV-Algebras by Regular Ultrapowers of [0, 1].Antonio Di Nola, Giacomo Lenzi & Luca Spada - 2010 - Archive for Mathematical Logic 49 (4):491-500.
    We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable (...)
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  4.  18
    Μ-Programs, Uniform Interpolation and Bisimulation Quantifiers for Modal Logics ★.Giovanna D'Agostino, Giacomo Lenzi & Tim French - 2006 - Journal of Applied Non-Classical Logics 16 (3-4):297-309.
    We consider the relation between the uniform interpolation property and the elimination of non-standard quantifiers (the bisimulation quantifiers) in the context of the ?-calculus. In particular, we isolate classes of frames where the correspondence between these two properties is nicely smooth.
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  5.  18
    On a Positive Set Theory with Inequality.Giacomo Lenzi - 2011 - Mathematical Logic Quarterly 57 (5):474-480.
    We introduce a quite natural Frege-style set theory, which we call Strong-Frege-2 equation image, a sort of simplification of the theory considered in 13 and 1 . We give a model of a weaker variant of equation image, called equation image, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Π11 sets of natural numbers; such an enumeration can be obtained via a classical priority argument much in the style of (...)
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  6.  16
    On Vaught’s Conjecture and Finitely Valued MV Algebras.Antonio Di Nola & Giacomo Lenzi - 2012 - Mathematical Logic Quarterly 58 (3):139-152.
    We show that the complete first order theory of an MV algebra has equation image countable models unless the MV algebra is finitely valued. So, Vaught's Conjecture holds for all MV algebras except, possibly, for finitely valued ones. Additionally, we show that the complete theories of finitely valued MV algebras are equation image and that all ω-categorical complete theories of MV algebras are finitely axiomatizable and decidable. As a final result we prove that the free algebra on countably many generators (...)
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  7.  12
    Deciding the Existence of Uniform Interpolants Over Transitive Models.Giovanna D’Agostino & Giacomo Lenzi - 2011 - Archive for Mathematical Logic 50 (1-2):185-196.
    We consider the problem of the existence of uniform interpolants in the modal logic K4. We first prove that all ${\square}$ -free formulas have uniform interpolants in this logic. In the general case, we shall prove that given a modal formula ${\phi}$ and a sublanguage L of the language of the formula, we can decide whether ${\phi}$ has a uniform interpolant with respect to L in K4. The ${\square}$ -free case is proved using a reduction to the Gödel Löb Logic (...)
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  8.  1
    Duality Theory and Skeleta for Semisimple MV-Algebras.Antonio Di Nola & Giacomo Lenzi - 2018 - Studia Logica 106 (6):1239-1260.
    We start from Marra–Spada duality between semisimple MV-algebras and Tychonoff spaces, and we consider the particular cases when the \-skeleta of the MV-algebras are restricted in some way. In particular we consider antiskeletal MV-algebras, that is, the ones whose \-skeleton is trivial.
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